Question

What inequalities would define region R?

Answer 1

The inequalities that define region R are: (a) r < R₁, (b) R₁ < r < R₂, and (c) r > R₂.

Step-by-step explanation:

To define region R, we need inequalities based on the given information. Let's assume that region R is defined by the condition (a < R₁, R₁ < r < R₂, and r > R₂).

Inequality (a) r < R₁ implies that any value of r less than R₁ is included in region R.

Inequality (b) R₁ < r < R₂ implies that any value of r between R₁ and R₂, but not including R₁ and R₂, is included in region R.

Inequality (c) r > R₂ implies that any value of r greater than R₂ is included in region R.

So, the inequalities that define region R are:

(a) r < R₁

(b) R₁ < r < R₂

(c) r > R₂

Answer 2

The inequalities that define region R are x ≥ 1, y ≥ 1, x ≤ 6, and y ≤ x.

Here are the inequalities that define the region R:

x ≥ 1: This is because the leftmost boundary of region R is at

x = 1.

y ≥ 1: This is because the bottommost boundary of region R is at

y = 1.

x ≤ 6: This is because the rightmost boundary of region R is at

x = 6.

y ≤ x: This is because the topmost boundary of region R is the line

y = x.

Therefore, the inequalities that define region R are x ≥ 1, y ≥ 1, x ≤ 6, and y ≤ x.